Simulation of groundwater age distributions
Simulation of groundwater age distributions
复制标题
地下水年龄分布的模拟
DOI：
10.1029/98wr02536
复制
发表时间：
1998
影响因子：
5.4
通讯作者：
J. Carrera
中科院分区：
文献类型：
--
作者：
M. Varni;J. Carrera
我们工作的目标是研究如何模拟地下水年龄，以便与实际测量结果进行比较。我们首先表明运动年龄的计算（通过沿着流线跟踪水获得的运动年龄的计算）在异质含水层中是不适定的。再加上它无法解释混合过程，使得它不足以与年龄测量值进行比较，年龄测量值是对水样中的年龄分布进行某种平均的结果（平均类型取决于测量程序）。因此，我们继续写出瞬态流动条件下停留时间累积分布函数的方程。这使我们能够推导出平均年龄及其分布的高阶矩的瞬态方程，从而概括了其他人之前的结果。这些矩可用于近似年龄测量，其不必等于水样的平均年龄。使用合成和真实的例子，我们表明在许多情况下，平均年龄是辐射年龄测量的可接受的估计。包括二阶校正（停留时间分布的方差）总是可以改善结果。另一方面，对于旧水（与半衰期相比），高阶近似收敛缓慢，以至于三阶近似常常使结果恶化。
The objective of our work is to examine how to simulate the age of groundwater in such a way that it can be compared to actual measurements. We start by showing that computation of kinematic age, the one obtained by tracking water along streamlines, is ill posed in heterogeneous aquifers. This, together with its inability to account for mixing processes, makes it inadequate for comparison with age measurements, which are the result of some averaging of the age distribution in the water sample (the type of averaging depends on the measurement procedure). Therefore we go on to write the equations for the cumulative distribution function of residence time under transient flow conditions. This allows us to derive transient equations for the mean age, as well as for the higher‐order moments of its distribution, which generalize previous results by others. These moments can be used for approximating age measurements, which need not be equal to the mean age of the water sample. Using both a synthetic and a real example, we show that mean age is an acceptable estimate of radiometric age measurements in many cases. Including a second‐order correction (variance of residence time distribution) always improves results. On the other hand, higher‐order approximations converge slowly for old (compared to half‐life) waters, to the point that third‐order approximations often worsen the results.